VGAM (version 0.8-2)

Zeta: The Zeta Distribution

Description

Density for the zeta distribution.

Usage

dzeta(x, p, log=FALSE)

Arguments

x

Numerical vector/matrix to evaluate the density.

p

The parameter $p$. This must be positive.

log

Logical. If log=TRUE then the logarithm of the density is returned.

Value

• Returns the density evaluated at x.

Warning

This function has not been fully tested.

Details

The density function of the zeta distribution is given by $$y^{-p-1} / \zeta(p+1)$$ where $p>0$, $y=1,2,\ldots$, and $\zeta$ is Riemann's zeta function.

References

Johnson N. L., Kotz S., and Balakrishnan N. (1993) Univariate Discrete Distributions, 2nd ed. New York: Wiley.

See Also

zeta, zetaff.

Examples

dzeta(1:20, p=2)
plot(1:6, dzeta(1:6, p=4), type="h", las=1, ylab="Probability",
     main="zeta probability function; black: p = 4; blue: p = 2")
points(0.10+1:6, dzeta(1:6, p=2), type="h", col="blue")